We are interested in studying the EE, MI and EoP in the (3+1)-dimensional non-conformal field theories using the framework of holography. Therefore, we start with a holographic background in five dimensions, which is called MAdS and its black hole version MBH. These backgrounds are dual to QCD-like theories at zero and finite temperature, respectively. MAdS background described by the following metric [1]}

ds2=r2R2g(r)(-dt2+dx2+R4r4dr2) ,      g(r)=erc2r2,      rc=R2c2,

and the MBH background is described by [2]}

ds2=r2R2g(r)(-f(r)dt2+dx2+R4r4f(r)dr2) ,      f(r)=1-rH4r4,

where \(\vec{x}\equiv (x,y,z)\) . \(r\)  is the radial coordinate, \(R\)  is the asymptotic AdS\(_5\)  radius supposed to be one hereafter and \(r_H\)  is the location of the horizon. The QCD-like model lives on the boundary at \(r\rightarrow \infty \) . \(r_c\)  is an lower bound on the minimum value of the radial coordinate which is related to the deformation parameter \(c\)  as \(r_c=R^2\sqrt{\frac{c}{2}}\) . From the trajectory of \(\rho \)  meson the value of \(c\)  is fixed and almost equals to \(0.9\)  GeV\(^2\)  [2]}. We assign an energy scale \(\Lambda _c\)  to \(r_c\)  which is defined \(\Lambda _c\equiv \sqrt{c}\) . Since \(c\)  has (energy)\(^2\)  dimension, \(\Lambda _c\)  has (energy) dimension. In the limit of \(c\rightarrow 0\) , the background () becomes AdS\(_5\)  and \(r\)  is not bounded [1]}. Also in this limit, the background () becomes AdS\(_5\)  black hole. In other words, in the \(c\rightarrow 0\ (\Lambda _c \rightarrow 0)\)  limit we have a conformal field theory. The thermodynamics properties of these backgrounds are studied in [5]} and some thermodynamics parameters such as entropy, density and pressure are expressed in terms of non-conformal parameters.
